It's almost this simple: there are two kinds of papers. Papers that kink from reasonably careful handling, and those that don't. Once you hit about 13 or 14 mils, kinking is not much of an issue.
However, if you like random, low frequency textures as on Fine Art Baryta and many quality matte art papers, that takes fairly thick papers to support the generation of those textures during manufacture. In that case thickness earns its keep.
My main objection to both thick and/or high gsm roll papers is that they have curl issues toward the end of a roll.
In the case of Canon iPF series, thick, stiff roll papers can also develop a pretty good curl in the curved path just before the printhead if they are parked in that position for a period of time. It's a nuisance to have to either discard 8 inches of paper, or do an in-printer decurl, or unload then reload the media between prints, one of which you should do to avoid head swipes at about the 7 inch position. With printers that have straighter feed paths, the main problem is that it's simply a nuisance to handle curly prints, except toward the end of the roll where head swipes are a problem with all printers, especially at higher altitudes where the available hold-down suction is reduced compared to sea level. None of that's a problem with reasonably thin papers.
IMHO, there is simply no excuse for thicknesses above 17 mils, or weight above about 300 gsm. Unless you are selling prints to people who like to feel them rather than look at them. But don't listen to me, I coat, mount, and frame almost everything as soon as I can can after printing. Bare prints are the Devil's playground.